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We present a robot-pose-registration algorithm, which is entirely based on large planar-surface patches extracted from point clouds sampled from a three-dimensional (3-D) sensor. This approach offers an alternative to the traditional point-to-point iterative-closest-point (ICP) algorithm, its point-to-plane variant, as well as newer grid-based algorithms, such as the 3-D normal distribution transform (NDT). The simpler case of known plane correspondences is tackled first by deriving expressions for least-squares pose estimation considering plane-parameter uncertainty computed during plane extraction. Closed-form expressions for covariances are also derived. To round-off the solution, we present a new algorithm, which is called minimally uncertain maximal consensus (MUMC), to determine the unknown plane correspondences by maximizing geometric consistency by minimizing the uncertainty volume in configuration space. Experimental results from three 3-D sensors, viz., Swiss-Ranger, University of South Florida Odetics Laser Detection and Ranging, and an actuated SICK S300, are given. The first two have low fields of view (FOV) and moderate ranges, while the third has a much bigger FOV and range. Experimental results show that this approach is not only more robust than point- or grid-based approaches in plane-rich environments, but it is also faster, requires significantly less memory, and offers a less-cluttered planar-patches-based visualization.